Question

A parallel beam of monochromatic light is incident normally on a slit. The diffraction pattern is observed on a screen placed at the focal plane of a convex lens. If the slit width is increased, the central maximum of the diffraction pattern will

• A. become broader and fainter
• B. become broader and brighter
• C. become narrower and fainter
• D. become narrower and brighter

Hint:

Central maximum width is inversely proportional to slit width.

Answer 1

The Correct Option is D

To solve this problem, we need to understand the phenomenon of diffraction, particularly how the diffraction pattern changes when the slit width is varied. Let's walk through the underlying physics and how they relate to the central diffraction maximum:

1. The formula used to determine the width of the central diffraction maximum is based on the single-slit diffraction pattern formula: \(a \sin \theta = m \lambda\), where \(a\) is the slit width, \(\lambda\) is the wavelength of light, \(\theta\) is the diffraction angle, and \(m\) is the order of the minimum.
2. The angular width of the central maximum (\(\Delta \theta\)) is given by the angle between the first minima on either side: \(\Delta \theta = 2 \sin^{-1}(\frac{\lambda}{a})\).
3. As the slit width \(a\) increases, the value of \(\frac{\lambda}{a}\) decreases, leading to a decrease in \(\Delta \theta\). This means the angular width of the central maximum becomes narrower.
4. A narrower central maximum implies that more light is concentrated into a smaller area, making it brighter.

Summarizing the analysis, if the slit width is increased, the central maximum of the diffraction pattern becomes narrower due to the geometry of diffraction and brighter because the same amount of light is concentrated into a smaller area.

Therefore, the correct answer is: "become narrower and brighter".